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Tan theta/(1-cot theta) + cotton theta/(1-tan theta) =(1+sec theta . Cosec theta) |
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Answer» Step-by-step EXPLANATION: tanx/(1-cotx) + cotx/(1-tanx) =(1+secx.cosecx) L.H.S = tanx/(1-cotx) +cotx/(1-tanx) :- tanx = SINX/cosx :-cotx = cosx/sinx (sinx/cosx)/(sinx-cosx)/sinx + (cosx/sinx)/(cosx-sinx)/cosx sin²x/cosx(sinx-cosx) -cos²x/sinx(sinx-cosx) (sin³x-cos³x)/sinxcosx (sinx-cosx) :- (a³-b³)=(a-b)(a²+ab+b²) {(sinx-cosx)(sin²x+sinxcosx+cos²x)/sinx(sinx-cosx) :- sin²x+cos²x =1 (1+sinxcosx)/sinxcosx 1/sinxcosx +sinxcosx/sinxcosx 1 + secx.cosecx PROVED hope it helps THANKU |
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